关于不定方程｛sum from (i=1) to k(1/x_i)-(1/x_i…x_k)｝=1

ON THE EQUATION ∑hi=11x i-1x 1…x k=1

讨论一类不定方程∑ｋｉ＝１１ｘｉ－１ｘｉ…ｘｋ＝１（ｋ≥３），给出了这类方程的两个重要性质，即方程的解序列的递归性和求解的一个充要条件，这就得出了一个对任意ｋ通用的求解方法。

The author discussed the integral solutions of the equation ∑ki=11x i+1x 1…x k=1. And gave two important properties:The recursive property of the solution sequence and a sufficient and necessary condition of finding solutions.Additionary,all solutions of the equation when k=7 are given.